reserve i, j, m, n for Nat,
  z, B0 for set,
  f, x0 for real-valued FinSequence;

theorem
  dim (RealVectSpace(Seg n)) = n
proof
  reconsider B=RN_Base n as Subset of RealVectSpace(Seg n) by FINSEQ_2:93;
A1: for I being Basis of RealVectSpace(Seg n) holds n = card I
  proof
    let I be Basis of RealVectSpace(Seg n);
    B is Basis of RealVectSpace(Seg n) by Th44;
    then card B=card I by RLVECT_5:25;
    hence n = card I by Lm5;
  end;
  n in NAT by ORDINAL1:def 12;
  hence thesis by A1,RLVECT_5:def 2;
end;
